Hi Ashley. I don't know where you're going in France or what your travel style is, but if you are into yoga, you may not want David's fast-paced itinerary. I won't suggest an alternative itinerary, but here are a few things to consider.
If you are flying into Italy from the U.S., you'll probably be jetlagged and sleep-deprived. Rome is the worst place to start your trip. It's a big bustling city, easy to get lost, and the best of Rome is to see the sights, which you won't enjoy if you're dragging. Venice is just the opposite. Okay, it's easy to get lost, but fun wandering the back canals, and you are never far from the Grand Canal or a main street. It's the best place to start a trip, because you can take it easy and soak up the special atmosphere while adjusting to the time change.
Florence is all about Renaissance art and architecture. If you love it, 3 days in Florence is barely enough. If you don't, you can see the highlights in one day. Florence has more of a big-city feel than Venice.
For hostels, use hostelworld.com (there's another good site that's similar, but I don't know the name). You can find the hostels in every city, check rates, read descriptions and reviews. If you want a private room, you will need to book in advance. Be careful before you book to read the cancellation policy. Most allow you to cancel 2-7 days in advance without payment, but be sure before you commit.
You can see the sights in Verona as a day trip from Venice OR you can stop on the way between Rome/Florence and Venice. Store your luggage at the train station in the morning and pick it up in the evening.
In general I try to take evening trains to maximize sightseeing time. You can eat picnic dinners on the train and rest after a long day on your feet. Even early October can be pretty hot, which can wear you out. When you plan your itinerary, think in terms of nights, not days. Every time you switch hotels, you have to allow enough extra time to get to/from the hotel/train. Travel time really eats into sightseeing time. Also, check the hostel rules. Some are closed for several hours during the day, so you may not be able to store your bags before heading out to see the sights.
Lastly, there is so much to choose from in Italy, you won't be able to see it all no matter how many times you visit. Choose the places that most call to you and plan an itinerary that suits your travel style.